bin1 := (1,2)(3,5)(4,7)(6,10)(8,13)(9,15)(11,18)(12,20)(14,23)(17,27)(19,30)(22,
     33)(24,36)(25,37)(26,39)(28,42)(29,41)(31,46)(32,48)(34,51)(35,50)(38,56)
     (40,59)(43,62)(44,64)(45,66)(47,69)(49,72)(52,75)(53,77)(54,79)(55,81)
     (57,84)(58,86)(60,89)(61,91)(63,94)(67,98)(68,100)(70,103)(73,107)(74,
     109)(76,112)(80,116)(82,119)(83,121)(85,124)(87,126)(88,106)(90,130)(92,
     133)(93,135)(95,138)(96,140)(99,143)(101,145)(104,149)(105,150)(108,154)
     (110,157)(111,159)(113,162)(114,164)(115,165)(117,168)(118,170)(120,173)
     (122,176)(123,178)(125,181)(127,184)(128,186)(129,188)(131,191)(132,192)
     (134,195)(136,160)(137,180)(139,201)(141,204)(142,167)(144,196)(146,209)
     (147,211)(148,213)(151,217)(152,219)(153,221)(155,224)(156,225)(158,228)
     (161,215)(163,234)(166,238)(169,229)(171,243)(172,245)(175,247)(177,250)
     (179,253)(182,257)(183,259)(185,262)(187,264)(189,267)(190,269)(193,273)
     (194,275)(197,277)(198,279)(199,281)(200,283)(202,235)(203,271)(205,289)
     (206,248)(207,292)(212,297)(214,299)(216,301)(218,304)(220,306)(222,309)
     (223,311)(226,315)(227,317)(230,320)(231,322)(232,324)(233,326)(236,313)
     (237,331)(239,334)(240,336)(241,338)(242,340)(244,343)(246,346)(249,350)
     (251,347)(252,353)(254,349)(255,357)(256,359)(258,362)(260,364)(261,366)
     (263,369)(265,371)(266,372)(268,375)(270,378)(272,381)(274,384)(276,387)
     (278,390)(280,393)(282,395)(284,398)(285,400)(286,402)(287,403)(288,405)
     (290,335)(291,365)(293,388)(294,410)(295,411)(296,413)(298,406)(300,418)
     (302,351)(303,422)(305,425)(308,428)(310,431)(312,434)(314,437)(316,440)
     (318,443)(319,445)(321,448)(323,451)(325,453)(327,456)(328,458)(329,460)
     (330,461)(332,464)(333,466)(337,421)(339,446)(341,473)(342,475)(344,478)
     (345,479)(348,482)(352,487)(354,490)(355,492)(356,494)(358,496)(361,500)
     (363,502)(367,488)(370,508)(373,511)(374,513)(376,515)(380,519)(382,522)
     (383,524)(385,527)(386,528)(389,532)(391,535)(392,450)(394,538)(396,541)
     (397,542)(399,545)(401,548)(404,552)(408,555)(409,557)(412,561)(414,564)
     (415,566)(416,474)(417,569)(419,572)(420,574)(423,567)(426,581)(427,583)
     (429,586)(430,588)(432,591)(436,595)(438,589)(439,599)(441,602)(442,603)
     (444,606)(447,610)(449,613)(452,563)(454,619)(455,620)(457,623)(459,626)
     (462,630)(467,636)(468,638)(469,640)(470,641)(471,643)(472,590)(477,649)
     (480,653)(481,651)(483,656)(484,658)(485,659)(486,661)(489,664)(493,669)
     (495,672)(497,675)(498,676)(499,678)(503,575)(504,684)(505,685)(506,687)
     (509,670)(510,692)(512,695)(514,698)(516,517)(518,703)(520,705)(521,707)
     (523,709)(525,712)(526,714)(529,718)(530,720)(531,722)(533,725)(534,726)
     (536,729)(537,716)(539,732)(540,713)(543,737)(544,739)(547,742)(549,745)
     (550,700)(551,748)(553,751)(554,715)(558,644)(559,756)(560,758)(562,761)
     (565,765)(568,768)(570,771)(571,773)(573,776)(576,779)(577,780)(578,782)
     (579,784)(582,772)(585,790)(587,793)(592,593)(594,801)(596,803)(597,805)
     (598,807)(600,810)(601,812)(604,815)(605,817)(607,820)(608,821)(609,823)
     (611,826)(612,828)(614,830)(615,797)(616,813)(617,833)(618,835)(621,839)
     (622,841)(625,844)(627,847)(628,798)(629,849)(631,852)(632,853)(633,855)
     (634,857)(635,858)(637,860)(639,863)(645,869)(646,871)(647,872)(648,874)
     (652,879)(654,882)(655,884)(657,887)(660,763)(662,893)(663,894)(665,897)
     (666,899)(667,901)(668,902)(671,889)(673,907)(674,909)(679,914)(680,915)
     (681,917)(682,723)(683,920)(686,923)(688,926)(689,927)(690,929)(691,931)
     (693,933)(694,935)(696,938)(697,939)(699,942)(701,945)(702,721)(704,802)
     (706,951)(708,952)(710,955)(711,956)(717,960)(719,963)(724,968)(727,936)
     (728,973)(730,976)(731,978)(733,947)(734,895)(735,975)(736,918)(738,986)
     (740,989)(741,991)(743,994)(744,996)(746,999)(747,1000)(749,940)(750,
     1003)(752,1006)(753,1008)(754,1010)(755,1012)(757,1015)(759,1017)(760,
     1019)(764,1022)(766,1025)(767,946)(769,1029)(770,1030)(774,1032)(775,
     1034)(777,967)(778,1038)(781,1042)(783,1045)(785,1047)(786,862)(787,1050)
     (788,1051)(789,1053)(791,1056)(792,1057)(794,1059)(795,1060)(796,1062)
     (799,1065)(800,822)(804,1071)(806,1073)(808,1076)(809,1077)(811,1079)
     (814,1082)(816,1085)(818,1088)(819,1090)(824,831)(825,1094)(827,1097)
     (829,1099)(832,1103)(834,1067)(836,1091)(837,1101)(838,1109)(840,1112)
     (842,1115)(843,1117)(845,1069)(846,1121)(848,1124)(850,1126)(851,1128)
     (854,1131)(856,1064)(859,1136)(861,1139)(864,1089)(865,1134)(866,1144)
     (867,1146)(868,1148)(875,1156)(876,1157)(877,1159)(878,1152)(880,1162)
     (886,1169)(888,1172)(890,1174)(891,1176)(896,959)(898,1007)(903,1188)
     (904,1190)(906,1192)(908,1021)(910,1178)(911,1186)(912,1199)(913,1201)
     (916,1205)(919,1208)(921,1203)(922,1211)(924,1214)(925,1215)(928,1218)
     (930,1220)(932,1223)(934,1226)(937,1230)(941,1235)(943,1238)(944,1239)
     (948,1232)(949,1061)(950,1245)(953,1249)(954,1251)(957,1252)(958,1253)
     (961,1256)(962,1258)(964,1261)(965,1262)(966,972)(969,1013)(971,1269)
     (974,1272)(977,1274)(979,1026)(980,1229)(981,1279)(982,1265)(983,1281)
     (984,1283)(985,1285)(987,1287)(988,1288)(990,1116)(992,1292)(993,1294)
     (995,1297)(997,1300)(998,1301)(1001,1304)(1002,1244)(1004,1302)(1009,
     1312)(1011,1264)(1014,1161)(1018,1320)(1020,1323)(1023,1327)(1024,1046)
     (1027,1247)(1028,1331)(1031,1335)(1033,1324)(1035,1328)(1036,1333)(1037,
     1341)(1039,1344)(1041,1346)(1043,1349)(1044,1351)(1048,1356)(1052,1361)
     (1054,1364)(1055,1147)(1058,1367)(1063,1373)(1066,1193)(1068,1369)(1070,
     1378)(1072,1381)(1074,1384)(1075,1386)(1078,1389)(1080,1391)(1081,1392)
     (1083,1395)(1084,1397)(1086,1399)(1087,1400)(1092,1388)(1093,1406)(1095,
     1409)(1096,1410)(1098,1413)(1100,1416)(1102,1418)(1104,1420)(1105,1422)
     (1106,1423)(1107,1424)(1108,1426)(1110,1428)(1111,1430)(1113,1433)(1114,
     1434)(1118,1290)(1119,1370)(1120,1438)(1122,1441)(1123,1442)(1125,1445)
     (1127,1377)(1129,1443)(1132,1452)(1133,1453)(1135,1456)(1137,1459)(1140,
     1462)(1141,1464)(1142,1466)(1145,1469)(1149,1460)(1150,1474)(1151,1475)
     (1153,1477)(1154,1479)(1158,1482)(1163,1485)(1164,1487)(1165,1488)(1166,
     1490)(1167,1491)(1168,1267)(1170,1494)(1171,1493)(1173,1498)(1175,1500)
     (1177,1503)(1179,1497)(1180,1506)(1181,1508)(1182,1509)(1183,1511)(1184,
     1412)(1185,1495)(1187,1480)(1191,1519)(1194,1522)(1195,1523)(1197,1524)
     (1198,1526)(1200,1529)(1202,1532)(1204,1533)(1206,1536)(1207,1537)(1209,
     1540)(1210,1542)(1212,1250)(1213,1546)(1216,1538)(1219,1553)(1221,1555)
     (1222,1359)(1224,1559)(1225,1561)(1227,1564)(1228,1565)(1231,1568)(1233,
     1571)(1234,1573)(1236,1576)(1237,1577)(1240,1581)(1241,1582)(1243,1584)
     (1246,1578)(1248,1590)(1254,1596)(1255,1597)(1257,1396)(1259,1601)(1260,
     1603)(1263,1606)(1266,1609)(1268,1611)(1270,1614)(1271,1616)(1273,1419)
     (1275,1421)(1276,1621)(1277,1623)(1278,1625)(1280,1627)(1282,1342)(1284,
     1631)(1286,1634)(1289,1638)(1291,1640)(1293,1642)(1295,1645)(1296,1647)
     (1298,1439)(1299,1650)(1303,1636)(1305,1446)(1306,1655)(1307,1656)(1308,
     1657)(1309,1659)(1310,1661)(1311,1663)(1313,1666)(1314,1668)(1316,1612)
     (1317,1671)(1318,1673)(1319,1674)(1322,1435)(1325,1680)(1329,1684)(1330,
     1686)(1334,1476)(1336,1691)(1337,1693)(1338,1694)(1339,1696)(1340,1698)
     (1343,1702)(1345,1705)(1347,1708)(1348,1710)(1350,1712)(1353,1704)(1354,
     1716)(1357,1719)(1363,1425)(1365,1505)(1366,1725)(1368,1728)(1371,1731)
     (1372,1733)(1374,1735)(1376,1737)(1379,1734)(1380,1521)(1382,1742)(1383,
     1743)(1385,1745)(1387,1747)(1390,1751)(1393,1754)(1394,1756)(1398,1761)
     (1401,1764)(1402,1765)(1403,1767)(1404,1769)(1405,1771)(1407,1774)(1408,
     1776)(1411,1779)(1414,1783)(1415,1785)(1417,1788)(1427,1796)(1429,1798)
     (1431,1801)(1432,1547)(1436,1805)(1437,1592)(1440,1809)(1444,1804)(1447,
     1817)(1448,1819)(1449,1820)(1450,1822)(1451,1824)(1455,1828)(1457,1830)
     (1458,1832)(1461,1826)(1463,1837)(1467,1841)(1468,1842)(1470,1845)(1471,
     1847)(1478,1853)(1481,1857)(1483,1859)(1484,1780)(1486,1862)(1492,1867)
     (1496,1872)(1501,1877)(1502,1879)(1504,1683)(1507,1884)(1510,1670)(1512,
     1890)(1513,1892)(1514,1689)(1515,1894)(1516,1896)(1517,1898)(1518,1781)
     (1520,1900)(1525,1904)(1527,1906)(1528,1908)(1530,1628)(1531,1912)(1534,
     1914)(1535,1916)(1539,1790)(1541,1922)(1543,1925)(1544,1730)(1545,1595)
     (1548,1931)(1549,1933)(1550,1935)(1551,1936)(1552,1937)(1557,1940)(1558,
     1942)(1560,1945)(1562,1948)(1563,1950)(1566,1954)(1569,1958)(1570,1960)
     (1572,1962)(1574,1818)(1575,1965)(1579,1952)(1580,1848)(1583,1974)(1585,
     1608)(1586,1978)(1587,1979)(1588,1980)(1589,1981)(1591,1984)(1593,1858)
     (1594,1988)(1598,1992)(1599,1993)(1600,1707)(1602,1996)(1604,1971)(1605,
     1999)(1607,2002)(1610,2005)(1613,2009)(1615,2012)(1617,2015)(1618,2017)
     (1619,2019)(1620,1654)(1622,2023)(1624,1699)(1626,1902)(1629,2030)(1630,
     2031)(1632,2034)(1633,1917)(1637,2039)(1639,2041)(1641,2044)(1643,2047)
     (1644,2048)(1646,2051)(1648,2054)(1649,2056)(1651,1810)(1652,2058)(1653,
     2060)(1658,2066)(1660,1969)(1664,2070)(1665,2072)(1667,2003)(1669,1866)
     (1675,2078)(1676,2080)(1677,2082)(1678,2084)(1679,2086)(1681,2087)(1685,
     2091)(1687,1688)(1690,2008)(1692,2095)(1695,2098)(1697,2100)(1700,1910)
     (1701,1878)(1703,2105)(1706,2108)(1709,1915)(1711,2113)(1713,2115)(1714,
     2117)(1715,1748)(1718,2122)(1721,2124)(1722,1849)(1724,2123)(1726,2129)
     (1727,1871)(1729,2132)(1732,2135)(1736,2139)(1738,2142)(1739,2143)(1740,
     2145)(1741,2106)(1744,2150)(1746,2153)(1749,2156)(1750,2158)(1752,2152)
     (1753,2161)(1755,2164)(1757,2166)(1758,2168)(1759,2170)(1760,2171)(1762,
     2173)(1763,1835)(1766,2177)(1768,2179)(1770,2182)(1772,1784)(1773,2016)
     (1775,2187)(1777,2189)(1778,2125)(1782,2068)(1786,2198)(1787,2199)(1789,
     2201)(1791,2203)(1792,1816)(1793,2097)(1794,2205)(1795,1854)(1797,2208)
     (1799,2210)(1800,2211)(1802,2214)(1806,2219)(1807,2220)(1808,2222)(1811,
     1886)(1812,2227)(1813,2146)(1814,2230)(1815,2232)(1821,2237)(1823,2239)
     (1825,2241)(1827,2243)(1829,2245)(1831,2247)(1833,2250)(1834,2252)(1836,
     2254)(1838,1881)(1839,1864)(1840,2257)(1843,2018)(1844,2261)(1846,2188)
     (1850,1868)(1851,2265)(1852,2079)(1855,2270)(1856,2193)(1860,2266)(1861,
     2275)(1863,1990)(1865,2276)(1869,2283)(1874,2288)(1875,2120)(1880,2263)
     (1882,2292)(1883,2294)(1888,2300)(1889,2301)(1895,2305)(1897,2074)(1899,
     1939)(1901,2311)(1903,2313)(1905,2315)(1907,2317)(1909,2319)(1913,2323)
     (1918,2328)(1919,2330)(1920,2331)(1921,2333)(1923,2334)(1924,2304)(1927,
     2337)(1928,2297)(1929,2339)(1930,2341)(1932,1987)(1938,2347)(1941,2350)
     (1943,2353)(1944,2352)(1946,2356)(1947,2357)(1949,2360)(1951,2363)(1953,
     2366)(1955,2369)(1956,2371)(1957,2373)(1959,2376)(1961,1983)(1963,2380)
     (1964,2382)(1966,2385)(1967,2195)(1968,2109)(1970,2390)(1972,2393)(1973,
     2110)(1975,2280)(1976,2397)(1977,2398)(1982,2137)(1985,2065)(1986,2403)
     (1991,2407)(1994,2411)(1995,2362)(1997,2412)(1998,2413)(2000,2415)(2001,
     2186)(2004,2314)(2006,2419)(2007,2192)(2010,2422)(2011,2424)(2013,2426)
     (2014,2427)(2020,2432)(2021,2204)(2022,2436)(2024,2096)(2025,2438)(2026,
     2440)(2027,2442)(2028,2102)(2029,2444)(2032,2447)(2033,2449)(2036,2452)
     (2037,2454)(2038,2455)(2040,2217)(2042,2090)(2043,2457)(2045,2459)(2049,
     2464)(2050,2466)(2052,2434)(2053,2468)(2055,2202)(2057,2472)(2059,2473)
     (2061,2233)(2062,2476)(2063,2399)(2064,2478)(2067,2481)(2069,2483)(2071,
     2485)(2073,2404)(2075,2490)(2077,2492)(2083,2497)(2085,2499)(2088,2502)
     (2089,2308)(2093,2409)(2094,2332)(2099,2316)(2101,2498)(2103,2509)(2104,
     2511)(2111,2505)(2112,2518)(2114,2154)(2116,2522)(2118,2525)(2119,2526)
     (2121,2191)(2126,2532)(2130,2537)(2131,2539)(2133,2541)(2134,2542)(2136,
     2544)(2138,2416)(2140,2267)(2141,2549)(2144,2552)(2147,2556)(2148,2558)
     (2149,2560)(2151,2563)(2155,2367)(2157,2568)(2159,2461)(2160,2571)(2162,
     2574)(2163,2488)(2165,2575)(2167,2578)(2169,2580)(2172,2582)(2174,2584)
     (2176,2587)(2178,2400)(2180,2590)(2181,2592)(2183,2593)(2184,2595)(2185,
     2596)(2190,2599)(2194,2603)(2196,2604)(2197,2605)(2200,2533)(2206,2612)
     (2207,2282)(2209,2613)(2213,2374)(2215,2616)(2216,2617)(2221,2621)(2223,
     2623)(2224,2625)(2225,2364)(2226,2520)(2228,2312)(2229,2631)(2231,2632)
     (2234,2636)(2235,2637)(2236,2551)(2238,2641)(2240,2644)(2242,2515)(2244,
     2645)(2246,2417)(2248,2648)(2249,2649)(2251,2651)(2253,2394)(2255,2655)
     (2256,2489)(2259,2656)(2260,2658)(2262,2661)(2264,2663)(2268,2668)(2271,
     2602)(2272,2671)(2273,2361)(2274,2673)(2277,2676)(2279,2443)(2284,2682)
     (2285,2684)(2286,2287)(2289,2687)(2290,2689)(2291,2691)(2295,2693)(2296,
     2695)(2298,2565)(2299,2697)(2302,2653)(2303,2699)(2306,2530)(2307,2395)
     (2310,2519)(2318,2705)(2320,2702)(2321,2708)(2322,2710)(2324,2712)(2326,
     2714)(2327,2716)(2329,2719)(2335,2725)(2336,2726)(2338,2729)(2340,2732)
     (2342,2620)(2343,2735)(2344,2737)(2345,2739)(2346,2740)(2348,2690)(2349,
     2744)(2351,2747)(2355,2749)(2359,2465)(2365,2755)(2368,2758)(2370,2761)
     (2372,2763)(2377,2769)(2378,2562)(2379,2772)(2381,2774)(2383,2776)(2384,
     2778)(2386,2781)(2387,2783)(2389,2786)(2391,2788)(2392,2766)(2396,2791)
     (2401,2794)(2402,2796)(2405,2800)(2406,2802)(2410,2610)(2414,2809)(2418,
     2812)(2420,2814)(2421,2816)(2423,2819)(2425,2821)(2428,2824)(2429,2826)
     (2430,2828)(2431,2829)(2433,2832)(2435,2833)(2437,2835)(2439,2838)(2441,
     2841)(2445,2608)(2446,2536)(2448,2846)(2450,2848)(2451,2850)(2453,2852)
     (2456,2855)(2458,2857)(2462,2503)(2463,2861)(2467,2730)(2469,2867)(2470,
     2722)(2471,2869)(2474,2871)(2475,2873)(2477,2876)(2479,2879)(2480,2875)
     (2482,2543)(2484,2811)(2487,2884)(2491,2607)(2494,2889)(2495,2890)(2501,
     2893)(2504,2615)(2506,2545)(2507,2898)(2508,2528)(2510,2902)(2512,2905)
     (2513,2907)(2514,2577)(2516,2909)(2517,2700)(2521,2913)(2523,2588)(2524,
     2915)(2527,2916)(2529,2917)(2534,2921)(2535,2922)(2538,2925)(2540,2927)
     (2546,2931)(2547,2550)(2548,2933)(2553,2752)(2554,2630)(2555,2939)(2557,
     2940)(2559,2942)(2561,2566)(2564,2718)(2567,2949)(2572,2614)(2573,2953)
     (2579,2639)(2581,2830)(2583,2962)(2585,2965)(2586,2966)(2589,2969)(2591,
     2971)(2594,2973)(2597,2977)(2598,2978)(2600,2981)(2606,2985)(2609,2987)
     (2611,2864)(2618,2853)(2619,2956)(2622,2998)(2624,3000)(2626,3002)(2627,
     2756)(2628,3004)(2629,3006)(2633,3010)(2634,3011)(2635,3012)(2638,2938)
     (2640,3018)(2642,3021)(2643,3014)(2646,2667)(2647,2825)(2650,3025)(2652,
     2918)(2654,3028)(2657,3030)(2660,3033)(2662,2976)(2664,2845)(2665,2754)
     (2666,2967)(2669,3039)(2670,3040)(2674,3044)(2675,2961)(2679,2934)(2680,
     3024)(2681,2926)(2683,2701)(2685,3051)(2686,3052)(2688,2952)(2692,2860)
     (2694,3058)(2696,3059)(2698,2803)(2703,2842)(2704,2919)(2706,3063)(2709,
     2801)(2711,3068)(2713,3071)(2715,3074)(2717,3077)(2720,3080)(2721,2870)
     (2723,3082)(2724,3084)(2727,2896)(2731,3089)(2733,3013)(2734,3091)(2736,
     3094)(2741,3092)(2742,3045)(2745,2982)(2746,3099)(2748,3101)(2750,2930)
     (2751,3105)(2753,3108)(2757,3111)(2759,3113)(2760,3114)(2762,2932)(2764,
     2858)(2765,3117)(2767,3109)(2768,3116)(2770,3122)(2771,3123)(2773,3126)
     (2775,3127)(2777,3073)(2779,3132)(2780,3134)(2782,3137)(2784,3139)(2785,
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